Question 1

Solve the system of equations by the elimination method.
-$$\begin{array} { c } 
x + 3 y = 15 \
- 6 x + 4 y = 20
\end{array}$$

Accepted Answer

A)  no solution 
B)  $( 1,4 )$ 
C)  $( - 5,0 )$ 
D)  $( 0,5 )$ 
A)  no solution 
B)  $( 1,4 )$ 
C)  $( - 5,0 )$ 
D)  $( 0,5 )$

Question 2

Solve by the substitution method.
-$$\begin{array} { l } 
8 x + 17 = 9 y \
- 6 x - 2 y = 4
\end{array}$$

Accepted Answer

A)  $( - 1,2 )$ 
B)  No solution 
C)  $( - 2,2 )$ 
D)  $( - 1,1 )$ 
A)  $( - 1,2 )$ 
B)  No solution 
C)  $( - 2,2 )$ 
D)  $( - 1,1 )$

Question 3

Solve the problem.
-Two angles have a sum of $81 ^ { \circ }$. Their difference is $15 ^ { \circ }$. Find the angles.

Accepted Answer

A)  $67 ^ { \circ }$ and $14 ^ { \circ }$ 
B)  $35 ^ { \circ }$ and $50 ^ { \circ }$ 
C)  $48 ^ { \circ }$ and $33 ^ { \circ }$ 
D)  $46 ^ { \circ }$ and $35 ^ { \circ }$ 
A)  $67 ^ { \circ }$ and $14 ^ { \circ }$ 
B)  $35 ^ { \circ }$ and $50 ^ { \circ }$ 
C)  $48 ^ { \circ }$ and $33 ^ { \circ }$ 
D)  $46 ^ { \circ }$ and $35 ^ { \circ }$

Question 4

Solve the system of equations by the elimination method.
-$$\begin{array} { l } 
5 x - 6 y = - 5 \
15 x - 18 y = 15
\end{array}$$

Accepted Answer

A)  no solution 
B)  $( 25 , - 30 )$ 
C)  infinitely many solutions 
D)  $( - 25,30 )$ 
A)  no solution 
B)  $( 25 , - 30 )$ 
C)  infinitely many solutions 
D)  $( - 25,30 )$

Question 5

Solve by the substitution method.
-$$\begin{array} { r } 
x + 3 y = 18 \
7 x + 4 y = 24
\end{array}$$

Accepted Answer

A)  $( 0,6 )$ 
B)  No solution 
C)  $( - 6,0 )$ 
D)  $( 1,5 )$ 
A)  $( 0,6 )$ 
B)  No solution 
C)  $( - 6,0 )$ 
D)  $( 1,5 )$

Question 6

Solve using the elimination method.
-$$\begin{array} { c } 
x + 6 y = 26 \
2 x + 6 y = 22
\end{array}$$

Accepted Answer

A)  $( 4,4 )$ 
B)  No solution 
C)  $( - 4,5 )$ 
D)  $( - 3 , - 4 )$ 
A)  $( 4,4 )$ 
B)  No solution 
C)  $( - 4,5 )$ 
D)  $( - 3 , - 4 )$

Question 7

Solve.
-From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 69 miles apart?

Accepted Answer

A) 5 hours 
B) 1 hour 
C) 4 hours 
D) 3 hours 
A) 5 hours 
B) 1 hour 
C) 4 hours 
D) 3 hours

Question 8

Solve by the substitution method.
-$$\begin{array} { c } 
x + y = 7 \
5 x + 5 y = 35
\end{array}$$

Accepted Answer

A)  $( 0,0 )$ 
B)  Infinite number of solutions 
C)  $( 7,5 )$ 
D)  $( 8 , - 1 )$ 
A)  $( 0,0 )$ 
B)  Infinite number of solutions 
C)  $( 7,5 )$ 
D)  $( 8 , - 1 )$

Question 9

Solve the problem.
-Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $\$ 5.00$, how many of the coins are nickels?

Accepted Answer

A)  23 nickels 
B)  10 nickels 
C)  12 nickels 
D)  18 nickels 
A)  23 nickels 
B)  10 nickels 
C)  12 nickels 
D)  18 nickels

Question 10

Solve the problem.
-A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $9 \%$ cement should he mix with 10 bags of $10.8 \%$ cement to produce a mix containing $10 \%$ cement?

Accepted Answer

A)  23 bags 
B)  10 bags 
C)  8 bags 
D)  18 bags 
A)  23 bags 
B)  10 bags 
C)  8 bags 
D)  18 bags

Question 11

Solve graphically.
-$\begin{array}{l}
2 x+y=6 \
4 x+2 y=12
\end{array}$

Accepted Answer

A)  No solution 
B)  Infinite number of solutions 
C)  $( 0,6 )$ 
D)  $( 5 , - 4 )$ 
A)  No solution 
B)  Infinite number of solutions 
C)  $( 0,6 )$ 
D)  $( 5 , - 4 )$

Question 12

Solve.
-$\begin{array} { l } 
x + y + z = 1 \
x - y + 3 z = - 13 \
5 x + y + z = 9
\end{array}$

Accepted Answer

A)  $( - 4,2,3 )$ 
B)  $( - 4,3,2 )$ 
C)  No solution 
D)  $( 2,3 , - 4 )$ 
A)  $( - 4,2,3 )$ 
B)  $( - 4,3,2 )$ 
C)  No solution 
D)  $( 2,3 , - 4 )$

Question 13

Solve the problem.
-Ellen wishes to mix candy worth $\$ 1.79$ per pound with candy worth $\$ 3.75$ per pound to form 22 pounds of a mixture worth $\$ 2.95$ per pound. How many pounds of the more expensive candy should she use?

Accepted Answer

A)  13 pounds 
B)  11 pounds 
C)  9 pounds 
D)  18 pounds 
A)  13 pounds 
B)  11 pounds 
C)  9 pounds 
D)  18 pounds

Question 14

Solve the problem.
-Mardi received an inheritance of $\$ 60,000$. She invested part at $8 \%$ and deposited the remainder in tax-free bonds at $11 \%$. Her total annual income from the investments was $\$ 5700$. Find the amount invested at $8 \%$.

Accepted Answer

A)  $\$ 54,300$ 
B)  $\$ 29,000$ 
C)  $\$ 30,000$ 
D)  $\$ 15,000$ 
A)  $\$ 54,300$ 
B)  $\$ 29,000$ 
C)  $\$ 30,000$ 
D)  $\$ 15,000$

Question 15

Solve the problem using the elimination method.
-The sum of two numbers is 41 . The larger number minus the smaller number is 9 . What are the numbers?

Accepted Answer

A)  18 and 27 
B)  25 and 16 
C)  33 and 8 
D)  23 and 18 
A)  18 and 27 
B)  25 and 16 
C)  33 and 8 
D)  23 and 18

Question 16

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l } 
3 x = y + 3 \
6 x - 2 y = 3
\end{array}$$

Accepted Answer

A)  Inconsistent and dependent 
B)  Consistent and independent 
C)  Inconsistent and independent 
D)  Consistent and dependent 
A)  Inconsistent and dependent 
B)  Consistent and independent 
C)  Inconsistent and independent 
D)  Consistent and dependent

Question 17

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c } 
- 10 x - 2 y = 10 \
5 x - y = - 5
\end{array}$$

Accepted Answer

A)  Consistent and independent 
B)  Inconsistent and independent 
C)  Inconsistent and dependent 
D)  Consistent and dependent 
A)  Consistent and independent 
B)  Inconsistent and independent 
C)  Inconsistent and dependent 
D)  Consistent and dependent

Question 18

Solve the problem.
-Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

Accepted Answer

A) 23 tickets 
B) 18 tickets 
C) 7 tickets 
D) 9 tickets 
A) 23 tickets 
B) 18 tickets 
C) 7 tickets 
D) 9 tickets

Question 19

Solve the system of equations by the elimination method.
-$$\begin{array} { l } 
\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 18 \
\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 9
\end{array}$$

Accepted Answer

A)  $( - 12,0 )$ 
B)  $( 0 , - 12 )$ 
C)  $( 0,12 )$ 
D)  $( 12,0 )$ 
A)  $( - 12,0 )$ 
B)  $( 0 , - 12 )$ 
C)  $( 0,12 )$ 
D)  $( 12,0 )$

Question 20

Solve graphically.
-$\begin{array}{l}
x=-y \
y+x=6
\end{array}$

Accepted Answer

A)  $( 1,5 )$ 
B)  No solution 
C)  $( 1,1 )$ 
D)  Infinite number of solutions 
A)  $( 1,5 )$ 
B)  No solution 
C)  $( 1,1 )$ 
D)  Infinite number of solutions

Solve the system of equations by the elimination method. - x+3y=15 -6x+4y=20

Solve by the substitution method. - 8x+17=9y -6x-2y=4

Solve the problem. -Two angles have a sum of $81 ^ { \circ }$ . Their difference is $15 ^ { \circ }$ . Find the angles.

Solve the system of equations by the elimination method. - 5x-6y=-5 15x-18y=15

Solve by the substitution method. - x+3y=18 7x+4y=24

Solve using the elimination method. - x+6y=26 2x+6y=22

Solve. -From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 69 miles apart?

Solve by the substitution method. - x+y=7 5x+5y=35

Solve the problem. -Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $\$ 5.00$ , how many of the coins are nickels?

Solve the problem. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $9 \%$ cement should he mix with 10 bags of $10.8 \%$ cement to produce a mix containing $10 \%$ cement?

Solve graphically. - 2x+y=6 4x+2y=12 $Solve graphically. - \begin{array}{l} 2 x+y=6 \\ 4 x+2 y=12 \end{array}$

Solve. - x+y+z=1 x-y+3z=-13 5x+y+z=9

Solve the problem. -Ellen wishes to mix candy worth $\$ 1.79$ per pound with candy worth $\$ 3.75$ per pound to form 22 pounds of a mixture worth $\$ 2.95$ per pound. How many pounds of the more expensive candy should she use?

Solve the problem. -Mardi received an inheritance of $\$ 60,000$ . She invested part at $8 \%$ and deposited the remainder in tax-free bonds at $11 \%$ . Her total annual income from the investments was $\$ 5700$ . Find the amount invested at $8 \%$ .

Solve the problem using the elimination method. -The sum of two numbers is 41 . The larger number minus the smaller number is 9 . What are the numbers?

Classify the system as consistent or inconsistent, and dependent or independent. - 3x=y+3 6x-2y=3

Classify the system as consistent or inconsistent, and dependent or independent. - -10x-2y=10 5x-y=-5

Solve the problem. -Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

Solve the system of equations by the elimination method. - x-y=-18 x+y=-9

Solve graphically. - x=-y y+x=6 $Solve graphically. - \begin{array}{l} x=-y \\ y+x=6 \end{array}$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

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Exam 8: Systems of Equations